---
res:
bibo_abstract:
- We consider random matrices of the form H=W+λV, λ∈ℝ+, where W is a real symmetric
or complex Hermitian Wigner matrix of size N and V is a real bounded diagonal
random matrix of size N with i.i.d.\ entries that are independent of W. We assume
subexponential decay for the matrix entries of W and we choose λ∼1, so that the
eigenvalues of W and λV are typically of the same order. Further, we assume that
the density of the entries of V is supported on a single interval and is convex
near the edges of its support. In this paper we prove that there is λ+∈ℝ+ such
that the largest eigenvalues of H are in the limit of large N determined by the
order statistics of V for λ>λ+. In particular, the largest eigenvalue of H
has a Weibull distribution in the limit N→∞ if λ>λ+. Moreover, for N sufficiently
large, we show that the eigenvectors associated to the largest eigenvalues are
partially localized for λ>λ+, while they are completely delocalized for λ<λ+.
Similar results hold for the lowest eigenvalues. @eng
bibo_authorlist:
- foaf_Person:
foaf_givenName: Jioon
foaf_name: Lee, Jioon
foaf_surname: Lee
- foaf_Person:
foaf_givenName: Kevin
foaf_name: Schnelli, Kevin
foaf_surname: Schnelli
foaf_workInfoHomepage: http://www.librecat.org/personId=434AD0AE-F248-11E8-B48F-1D18A9856A87
orcid: 0000-0003-0954-3231
bibo_doi: 10.1007/s00440-014-0610-8
bibo_issue: 1-2
bibo_volume: 164
dct_date: 2016^xs_gYear
dct_language: eng
dct_publisher: Springer@
dct_title: Extremal eigenvalues and eigenvectors of deformed Wigner matrices@
...